The Influence of Implicit Hand-Based Representations on Mental Arithmetic

Klein, Elise; Moeller, Korbinian; Hinckeldey, Klaus Willmes-von; Nuerk, Hans‐Christoph; Domahs, Frank

doi:10.3389/fpsyg.2011.00197

Cited by 68 publications

(67 citation statements)

References 43 publications

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“…Vinod Menon, a developmental cognitive neuroscientist at Stanford University in California, and his colleagues presented single-digit addition problems to 28 children aged 7-9, as well as to 20 adolescents aged 14-17 and 20 young adults. Consistent with previous psychology studies, the children relied heavily on counting out the sums, whereas adolescents and adults tended to draw on memorized information to calculate the answers (Klein et al, 2011).…”

Section: Introductionsupporting

confidence: 50%

How a brain says: Fingermath for Empowering Children’s Creativity

Yanuarto

2017

EduLearn

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Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis, or "finger sense," enhances mathematical skills. Therefore neurocognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development. However, research in mathematics education recommends fostering mentally based numerical representations so as to induce children to abandon finger counting. More precisely, mathematics education recommends first using finger counting, then concrete structured representations and, finally, mental representations of numbers to perform numerical operations. Taken together, these results reveal an important debate between neurocognitive and mathematics education research concerning the benefits and detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be discussed.

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Section: Introductionsupporting

confidence: 50%

How a brain says: Fingermath for Empowering Children’s Creativity

Yanuarto

2017

EduLearn

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“…Multiple studies have shown that finger counting habits influence number processing performance (Domahs et al 2010;Newman and Soylu 2014) and interact with visuospatial representations of numbers (Fischer 2008). Furthermore, there is evidence for adults' unconscious encoding of small numbers in the form of finger numeral representations (Badets et al 2010) and finger counting patterns affecting arithmetic performance based on a sub-base-five effect (Klein et al 2011). In multiple studies, it has been shown that finger sense (Fayol et al 1998;Noel 2005) and fine motor ability (Luo et al 2007) predict mathematical performance in young children.…”

Section: Introductionmentioning

confidence: 98%

Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study

Soylu

Newman

2015

Cogn Process

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Fingers are used as canonical representations for numbers across cultures. In previous imaging studies, it was shown that arithmetic processing activates neural resources that are known to participate in finger movements. Additionally, in one dual-task study, it was shown that anatomically ordered finger tapping disrupts addition and subtraction more than multiplication, possibly due to a long-lasting effect of early finger counting experiences on the neural correlates and organization of addition and subtraction processes. How arithmetic task difficulty and tapping complexity affect the concurrent performance is still unclear. If early finger counting experiences have bearing on the neural correlates of arithmetic in adults, then one would expect anatomically and non-anatomically ordered tapping to have different interference effects, given that finger counting is usually anatomically ordered. To unravel these issues, we studied how (1) arithmetic task difficulty and (2) the complexity of the finger tapping sequence (anatomical vs. non-anatomical ordering) affect concurrent performance and use of key neural circuits using a mixed block/event-related dual-task fMRI design with adult participants. The results suggest that complexity of the tapping sequence modulates interference on addition, and that one-digit addition (fact retrieval), compared to two-digit addition (calculation), is more affected from anatomically ordered tapping. The region-of-interest analysis showed higher left angular gyrus BOLD response for one-digit compared to two-digit addition, and in no-tapping conditions than dual tapping conditions. The results support a specific association between addition fact retrieval and anatomically ordered finger movements in adults, possibly due to finger counting strategies that deploy anatomically ordered finger movements early in the development.

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“…For instance, in a large cohort of primary schoolers, calculation errors frequently include the erratic assignment of full hands (i.e., 5 items; Domahs, Krinzinger, & Willmes, 2008). But also in adults, implicit hand-based magnitude representations were reported to produce increased calculation latencies when addition problems crossed the five-boundary (Klein, Moeller, Willmes, Nuerk, & Domahs, 2011). In Western groups, such sub-base-five effects had been particularly pronounced and it was concluded that finger experiences (i.e., counting habits) influence mental number representations (Domahs, Moeller, Huber, Willmes, & Nuerk, 2010).…”

Section: Different Shapes Of Categorical and Linear Spatial Mappingsmentioning

confidence: 99%

Space in numerical and ordinal information: A common construct?

2017

Self Cite

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Space is markedly involved in numerical processing, both explicitly in instrumental learning and implicitly in mental operations on numbers. Besides action decisions, action generations, and attention, the response-related effect of numerical magnitude or ordinality on space is well documented in the Spatial-Numerical Associations of Response Codes (SNARC) effect. Here, right-over left-hand responses become relatively faster with increasing magnitude positions. However, SNARC-like behavioral signatures in non-numerical tasks with ordinal information were also observed and inspired new models integrating seemingly spatial effects of ordinal and numerical metrics. To examine this issue further, we report a comparison between numerical SNARC and ordinal SNARC-like effects to investigate group-level characteristics and individual-level deductions from generalized views, i.e., convergent validity. Participants solved order-relevant (before/ after classification) and order-irrelevant tasks (font color classification) with numerical stimuli 1-5, comprising both magnitude and order information, and with weekday stimuli, comprising only ordinal information. A small correlation between magnitude-and order-related SNARCs was observed, but effects are not pronounced in order-irrelevant color judgments. On the group level, order-relevant spatialnumerical associations were best accounted for by a linear magnitude predictor, whereas the SNARC effect for weekdays was categorical. Limited by the representativeness of these tasks and analyses, results are inconsistent with a single amodal cognitive mechanism that activates space in mental processing of cardinal and ordinal information alike. A possible resolution to maintain a generalized view is proposed by discriminating different spatial activations, possibly mediated by visuospatial and verbal working memory, and by relating results to findings from embodied numerical cognition. Abstract concepts are often embedded into physical space: Numerical magnitudes increase to the right of a number line, weekdays are spatially organized in calendars, and the first step in a user manual is usually

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The Influence of Implicit Hand-Based Representations on Mental Arithmetic

Cited by 68 publications

References 43 publications

How a brain says: Fingermath for Empowering Children’s Creativity

How a brain says: Fingermath for Empowering Children’s Creativity

Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study

Space in numerical and ordinal information: A common construct?

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